SPATIAL PARTITIONING AND FUNCTIONAL SHAPE MATCHED DEFORMATION ALGORITHM FOR INTERACTIVE HAPTIC MODELING A dissertation presented to the faculty of the Russ College of Engineering and Technology of Ohio University In partial fulfillment of the requirements for the degree Doctor of Philosophy Wei Ji November 2008 © 2008 Wei Ji. All Rights Reserved. 2 This dissertation titled SPATIAL PARTITIONING AND FUNCTIONAL SHAPE MATCHED DEFORMATION ALGORITHM FOR INTERACTIVE HAPTIC MODELING by WEI JI has been approved for the School of Electrical Engineering and Computer Science and the Russ College of Engineering and Technology by Robert L. Williams II Professor of Mechanical Engineering Dennis Irwin Dean, Russ College of Engineering and Technology 3 Abstract JI, WEI, Ph.D., November 2008, Computer Science SPATIAL PARTITIONING AND FUNCTIONAL SHAPE MATCHED DEFORMATION ALGORITHM FOR INTERACTIVE HAPTIC MODELING (161 pp.) Director of Dissertation: Robert L. Williams II This dissertation focuses on the fast rendering algorithms on real-time 3D modeling. To improve the computational efficiency, binary space partitioning (BSP) and octree are implemented on the haptic model. Their features are addressed in detail. Three methods of triangle assignment with the splitting plane are discussed. The solutions for optimizing collision detection (CD) are presented and compared. The complexities of these partition methods are discussed, and recommendation is made. Then the deformable haptic model is presented. In this research, for the haptic modeling, the deformation calculation is only related to the graphics process because the haptic rendering is invisible and non-deformable rendering saves much computation cost. To achieve the fast deformation computation in the interactive simulation, the functional shape matched deformation (FSMD) algorithm is proposed for the tangential and normal components of the surface deformation. The benefit of the octree model is taken for searching the deformed area. To simplify the boundary of the deformed region, an ellipse deformation map is created based on the experimental data. The Gaussian radial 4 interpolation (GRI) is developed for building this map which is pre-computed. The FSMD algorithm is tested and considered feasible for the virtual haptic back (VHB) project. Moreover, some recommendations for the future work are suggested. Approved: _____________________________________________________________ Robert L. Williams II Professor of Mechanical Engineering 5 Acknowledgments I would initially like to thank my advisor Dr. Robert Williams for his constant support and insightful guidance for my master and doctoral studies throughout the past five years. He has provided me excellent opportunities to work with the virtual haptic back (VHB) research team. His theoretical knowledge helped me to solve many problems in my research work. I am deeply impressed by his patience and kindness. I would also like to express my thanks to Dr. John Howell, my college representative, for his support, many valuable suggestions on my research and his daily organization on the VHB project. I love working with him because of his enthusiasm for research and humor. I would additionally like to thank the members of my committee, Dr. Jundong Liu, Dr. Chang Liu and Dr. Frank Drews, for their instructions and time on my research. The knowledge gained from them will be my lifetime fortune. I, of course, am grateful to Dr. Sergio Lopez-Permouth for accepting to be my college representative and reviewing my dissertation. Many thanks go to the members of the VHB team: Bob Conatser, Ernur Karadogan, Meng-Yun Chen, Bajaj Kapil, David Noyes and Dr. Janet Burns. Finally, I express my deep thanks to my wife, Yan, and my two-year-old daughter, Eulina, for their love and support. Also I especially thank my parents and my sister for their encouragements. 6 Table of Contexts Abstract ............................................................................................................................... 3 List of Tables ....................................................................................................................... 9 List of Figures ................................................................................................................... 10 List of Abbreviations......................................................................................................... 13 1. Introduction ................................................................................................................ 14 1.1 Background of Deformation in Virtual Reality (VR) ........................................... 14 1.2 The Need for Deformation in the Virtual Haptic Back (VHB) Project ................ 16 1.3 Haptic and Graphic Renderings ........................................................................... 18 1.3.1 Haptic Rendering ........................................................................................... 18 1.3.2 Graphic Rendering ......................................................................................... 21 1.4 Literature Review ................................................................................................. 23 1.4.1 Deformation Algorithms ................................................................................ 23 1.4.1.1 Shape Interpolation (SI) .......................................................................... 23 1.4.1.2 Free-Form Deformation (FFD) ............................................................... 24 1.4.1.3 Skeleton-Subspace Deformation (SSD) .................................................. 26 1.4.1.4 Mass-Spring Model (MSM) .................................................................... 27 1.4.1.5 Finite Element Method (FEM) ................................................................ 29 1.4.1.6 Collision Detection (CD) ......................................................................... 30 1.4.2 Space Partition Methods ................................................................................ 31 1.4.2.1 Binary Space Partitioning (BSP) ............................................................. 31 1.4.2.2 Octree Partition ........................................................................................ 32 1.4.3 Major Area Discussions of Deformation Modeling ....................................... 32 1.5 Research Objectives ............................................................................................. 37 1.6 Dissertation Organization ..................................................................................... 38 2. Related Research Work .............................................................................................. 41 7 2.1 Haptic Model, Stiffness Map and Stereo Viewing System ................................... 41 2.2 Displacement Driven Force and Proxy Sphere ..................................................... 45 2.3 Non Deformable Modeling in Haptic Rendering ................................................. 47 2.4 Friction Effect in Tangential Deformation ........................................................... 49 2.5 Utility Libraries and Platform .............................................................................. 51 3. Spatial Partitioning for Fast Rendering ...................................................................... 52 3.1 Data Structure of the Haptic Model ...................................................................... 54 3.2 Rendering Performance Measurement ................................................................. 56 3.3 Binary Space Partitioning (BSP) for Haptic Rendering ....................................... 57 3.3.1 Construction of BSP Tree .............................................................................. 57 3.3.2 Triangles Distribution .................................................................................... 62 3.3.3 Haptic Detecting Box (HDB)......................................................................... 65 3.3.4 Performance and Complexity Analysis .......................................................... 70 3.4 Octree for Haptic Rendering ................................................................................ 75 3.4.1 Haptic Triangles Detection ............................................................................ 78 3.4.2 Complexity Analysis ...................................................................................... 79 4. Functional Shape Matched Deformation ................................................................... 84 4.1 Deformation Shape on Elastic Material ............................................................... 85 4.2 Normal Deformation ............................................................................................ 90 4.2.1 Normalized Gaussian Curve Mapping Array ................................................. 94 4.3 Tangential Deformation ........................................................................................ 99 4.4 Point Mapping to Ellipse Plane .......................................................................... 101 4.5 The Neighbor Nodes Ring Algorithm ................................................................ 106 4.6 Maximum Deformation ....................................................................................... 111 4.7 Visualization of Surface Strain ............................................................................112 5. Defined Deformation Boundary Shape .....................................................................115